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Correction:
\( \frac{dh}{dt} = -\frac{28.8}{25\pi} h^{-3/2} \) →
\( \int h^{3/2} dh = -\frac{28.8}{25\pi} \int dt \) →
\( \frac{2}{5} h^{5/2} = -\frac{28.8}{25\pi} t + C \)
At \( t = 0 \), \( h = 12 \): \( C = \frac{2}{5} \cdot 12^{5/2} \approx \frac{2}{5} \cdot 498.816 = 199.726 \)
At \( t = 10 \):
\( \frac{2}{5} h^{5/2} = 199.726 - \frac{28.8}{25\pi} \cdot 10 \)
\( \frac{28.8}{25\pi} \cdot 10 = \frac{288}{25\pi} \approx 3.648 \)
So \( \frac{2}{5} h^{5/2} = 199.726 - 3.648 = 196.078 \)
\( h^{5/2} = \frac{5}{2} \cdot 196.078 = 490.195 \)